Statistics Chapter 6

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Chapter 6

Techniques of statistical inference Using sample statistics to estimate the value of an unknown population parameter

Point estimate -- a single value estimate for a population parameter

The validity of an estimation method is increased when you use a sample statistic that is unbiased and has low variability.

A statistic is unbiased if it does not overestimate or underestimate the population parameter

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the sample mean is called the unbiased estimator of the population mean.

instead of estimating using a point estimate, estimate that the population mean lies in an interval. this is called an interval estimate (an interval or range of values used to estimate the population parameter.)

Interval estimate = point estimate +/- margin of error

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margin of error (maximum error of estimate or error tolerance) -- Greatest possible distance between the point estimate and value of the parameter being estimated, if we know the level of confidence and the population standard deviation.

level of confidence (c) -- the probability that the interval estimate contains the population parameter, assuming the estimation process is repeated a large number of times

critical values (Zc) -- separates sample statistics that are probable from those that are improbable

Margin of Error..... E= +/- (Zc) (Ox) IF 1. The sample is random

AND 2. the population is normally distributed

OR the sample size s 30 or greater

Interval estimate = Confidence interval

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Why do we use a margin of error?

Sampling error is the difference between the point estimate and the actual parameter

Sampling error = sample mean - population mean

However, since we do not know the population mean and the sample mean varies from sample to sample, we cannot find the sampling error.